The stabilized V-cycle method

Algebraic multilevel iterations methods are preconditioning algorithms, to solve elliptic type partial differential equations by iteration which can give both a robust and optimal, or nearly optimal, convergence rate and require per iteration step an arithmetic complexity proportional to the degree of freedoms in the problem. In addition, each iteration step can, in general, be implemented efficiently on massively parallel computers. To stabilize the condition number in the V-cycle version of the method one can use polynomial stabilization or inner solutions at certain, properly chosen levels in the multilevel hierarchy of meshes. The latter is considered here.